Cyclotron is a device used to accelerate heavy charged particles. It was invented by E.O. Lawrence and M.S. Livingston in 1934. In a cyclotron charged particles are made to move in a circular path using a magnetic field and they are accelerated by using electric field
Cyclotron consists of two semicircular hollow chambers known as Dees arranged in a perpendicular magnetic field. An ac of suitable frequency known as Cyclotron frequency is applied across the Dees.
Cyclotron consists of two semicircular hollow chambers known as Dees arranged in a perpendicular magnetic field. An ac of suitable frequency known as Cyclotron frequency is applied across the Dees.
Working
The charged particle to be accelerated is injected into the gap between the Dees. Due to the strong magnetic field the particle starts to move in a circular path. Now the electric field accelerates the particle and hence it starts to move in a circular path of increasing radius (spiral path).
As the particle move from one Dee towards the other the polarity of the Dees should change. The polarity of Dees should be changed at the same frequency as that of the revolution of the particle. Hence this frequency should be equal to the frequency of revolution of particle f=qB/2pixm. This frequency is known as the cyclotron frequency.
Kinetic Energy Gained by the Particle
In a cyclotron as speed increasing the radius of path also increases. So the maximum speed that can be gained by a cyclotron has a limit depending on the radius of the Dee. If R is the radius of the Dee then them maximum velocity that can be gain by a particle of charge q and mass m is vmax=qBR/m. Hence the maximum kinetic energy that can be gained is
K.E=1/2 mv2max=1/2m(qBR/m)2
Thus the kinetic energy that can be gained depends on mass of the particle magnetic field and radius of cyclotron. We have seen that the frequency of cyclotron is independent of speed of the particle. But as the particle gains extremely high velocity, relativistic effects come into play and its mass begins to increase. This will affect the normal working of cyclotron as frequency depends on the mass of the particle.
Yet another limitation of cyclotron is that very small particles like electron can not be accelerated using cyclotron. This is because as the mass of electron is very small the cyclotron frequency required becomes extremely high which is practically difficult.
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| Lorentz Force |
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| Force Acting on a current carrying conductor |
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